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cscθ
secθ
tanθ
cotθ
sin²θ
cos²θ
1
cot²θ
csc²θ
sec²θ
tan²θ
sinθ
1/cscθ
cosθ
1/secθ
secθ reciprocal identity
1/cosθ
cscθ reciprocal identity
1/sinθ
cotθ reciprocal identity
1/tanθ
tanθ quotient identity
sinθ/cosθ
cotθ quotient identity
cosθ/sinθ
-sinθ odd-even identity
sin(-θ)
cosθ odd-even identity
cos(-θ)
-tanθ odd-even identity
tan(-θ)
-cscθ odd-even identity
csc(-θ)
secθ odd-even identity
sec(-θ)
-cotθ odd-even identity
cot(-θ)
sinθ cofunction identity
cos (π/2-θ)
cosθ cofunction identity
sin (π/2-θ)
tanθ cofunction identity
cot (π/2-θ)
cscθ cofunction identity
sec (π/2-θ)
secθ cofunction identity
csc (π/2-θ)
cotθ cofunction identity
tan (π/2-θ)
sin²θ + cos²θ Pythagorean identity
1
1 + tan²θ Pythagorean identity
sec²θ
1 + cot²θ Pythagorean identity
csc²θ
sin(α + β) sum identity
sinαcosβ + cosαsinβ
sin(α - β) difference identity
sinαcosβ - cosαsinβ
cos(α + β) sum identity
cosαcosβ - sinαsinβ
cos(α - β) difference identity
cosαcosβ + sinαsinβ
tan(α + β) sum identity
tanα + tanβ/1 - tanαtanβ
tan(α - β) difference identity
tanα - tanβ/1 + tanαtanβ
sin 2θ double-angle identity
2 sinθcosθ
cos 2θ double-angle identity
cos²θ - sin²θ
2 cos²θ - 1
1 - 2 sin²θ
tan 2θ double-angle identity
2 tanθ/1 - tan²θ
sin½θ half-angle identity
±√1 - cosθ/2
cos½θ half-angle identity
±√1 + cosθ/2
tan½θ half-angle identity
±√1 - cosθ/1 + cosθ
1/sin x
csc x
1/cos x
sec x
1/tan x
cot x
1/csc x
sin x
1/sec x
cos x
1/cot x
tan x
sin²x+cos²x
1
1-cos²x
sin²x
1-sin²x
cos²x
1+tan²x
sec²x
1+cot²x
csc²x
sec²x-1
tan²x
csc²x-1
cot²x
sin(-x)
-sin x
csc(-x)
-csc x
cos(-x)
cos x
sec(-x)
sec x
tan(-x)
-tan x
cot(-x)
-cot x
sin(π/2-x)
cos x
cos(π/2-x)
sin x
tan(π/2-x)
cot x
csc(π/2-x)
sec x
sec(π/2-x)
csc x
cot(π/2-x)
tan x
sin x / cos x
tan x
cos x/ sin x
cot x
Identity (math)
A mathematical statement or equation that is true for any value.
Pythagorean Identities
A trigonometric identity that is derived using the Pythagorean Theorem.
a² + b² = c²
x² + y² = r²
sin²θ + cos²θ = 1 (y=sin, x=cos, r=1 on unit circle)
1 + cot²θ = csc²θ (divide everything by sin²θ)
tan²θ + 1 = sec²θ (divide everything by cos²θ)
Quotient
The answer to a division problem.
Quotient Identities
tanθ = sinθ/cosθ
cotθ = cosθ/sinθ
Reciprocal
One of a pair of numbers whose product is 1.
Reciprocal Identities
Expression
A mathematical statement (variables,numbers, and operation symbols) that does not contain an equal sign.
Equation
A mathematical statement that two expressions are equal.
Verify
To confirm or prove something is true.
Simplify
To make something easier or less complicated.
Solve
To find an answer to or explanation for a problem.
Evaluate
For a specific input, find the numerical output of an function. Plug a number in to get a solution.
Isolate
To get a variable alone in a mathematical equation.
Factor (verb)
To find the factors of a number or expression.
Factor (noun)
A number which divides into another number exactly without leaving a remainder.
Distribute (Expand)
Multiplying each term inside the parentheses with the term outside of the parentheses.
Combine Like Terms
Simplifying an expression by using mathematical operations of terms with the same variables and exponents.
Coefficient
A number multiplied by a variable in an algebraic expression.
Variable
A letter or symbol used to represent numbers in Algebra.
Constant
A value that does not change.
Radical
Another name for a root: one might refer to √2 as "radical 2."
Undefined
Having no solution.
(Examples: dividing by zero, negative square roots, the slope of a vertical line)
Domain
All the possible x-values that can be input into a function.
Range
All the possible y-values that can be the output of a function.
Inverse Function
The function obtained by switching the domain (x) and range (y) in a function.